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Much has changed in the world since William Pitt the Younger was prime minister and the United Kingdom was at war with Napoleon. But among the tax rules laid down by Her Majesty’s Revenue and Customs there remains a fiscal echo of those vanished days.

The “non-domicile” regime was originally introduced in 1799 to shelter those with foreign property from the UK’s newfangled wartime taxes. More than two centuries later, it still allows those who live in Britain to cite another country as their real domicile. Unlike other residents, they are only obliged to pay British tax on their overseas earnings if they remit that money to the UK.

In bygone days, when many subjects resided in colonies overseas, this may have had some slender justification. In modern Britain, it has none.

The rule is exploited by jet-setters and wealthy business executives to pick and choose the least fiscally burdensome domicile while continuing to enjoy the right to reside and work in Britain. Their numbers have been rising: from 83,000 in 1997 to 116,000 in 2013. Some, such as foreigners temporarily resident in Britain for work, may have a case for doing so. Far more dubious are cases where the individual is a long-term UK resident, or a British citizen who has elected — either through inheritance or from choice — to domicile themselves in a low-tax country.

This anomaly has been highlighted in recent days by the case of HSBC’s chief executive, Stuart Gulliver. While a British citizen born and raised in the UK, Mr Gulliver badged himself as domiciled in the low-tax haven of Hong Kong. Yet not only has Mr Gulliver worked in Britain for the past 12 years, he has also retained links with the UK, for instance sending his children to school there. Whether or not the arcane rules have been obeyed, this hardly counts as severing all ties.

It is hard to know how much the Treasury is losing out. There are no reliable figures for tax foregone. But the inherent unfairness of allowing the richest in society to avoid paying their fair share of tax has become a matter of fierce public irritation.

Tolerance was fraying even before the financial crisis. The Treasury looked at abolishing non-dom status on several occasions. But each time it drew back for fear of the consequences for Britain’s economy and the City of London in particular. These fears, however, are overdone.

Those who defend the status quo argue it promotes inward investment because wealthy non-doms build up assets in the UK simply by being here. Were it scrapped, they say, these individuals would leave, taking their enterprise and what UK tax they pay.

But in reality non-doms have few incentives to engage in UK activity. The chancellor George Osborne may have introduced measures to encourage them to remit from abroad to invest. But for the most part bringing offshore cash into Britain simply ensures that it will be taxed at UK rates.

As for the idea that abolition will trigger a flood of non-doms seeking sanctuary in Switzerland, some footloose individuals may leave. But the many advantages of London as a financial centre do not dissolve simply because of a change in a hitherto generous tax treatment of resident non domiciles. Low-tax cantons cannot match the City’s deep pool of financial expertise or the excitement of London life.

Both main political parties have recognised the indefensibility of the regime. But rather than abolish it, they have sought to raise its cost. Annual charges of £30,000 are levied on people who have been in the UK for more than seven years, rising to £50,000 (soon to be £60,000) for those with over 12 years’ residence. But while these have cut the take-up, they have not dealt with the intrinsic unfairness.

Britain should sweep away the archaism that allows people to claim a domicile that differs from nationality or residence. Few other civilised countries feel the need to offer such privileges to the wealthy. Liability to taxation should be solely based on residence. There can still be a grace period for foreign nationals posted temporarily to the UK before they are obliged to pay British tax.

More than two centuries after the introduction of income tax by Mr Pitt, his successors should end the egregious situation where the wealthiest enjoy the privileges of UK residency without paying their fair dues to the exchequer. The anomaly of non-dom status cannot be defended. It should be scrapped.